A nonlinear harmonic balance technique for the analysis of aerodynamic asymmetry of unsteady flows in turbomachinery is presented. The present method uses a mixed time-domain/frequency-domain approach that allows one to compute the unsteady aerodynamic response of turbomachinery blades to self-excited vibrations. Traditionally, researchers have investigated the unsteady response of a blade row with the assumption that all the blades in the row are identical. With this assumption the entire wheel can be modeled using complex periodic boundary conditions and a computational grid spanning a single blade passage. In this study, the steady/unsteady aerodynamic asymmetry is modeled using multiple passages. Specifically, the method has been applied to aerodynamically asymmetric flutter problems for a rotor with a symmetry group of 2. The effect of geometric asymmetries on the unsteady aerodynamic response of a blade row is illustrated. For the cases investigated in this paper, the change in the diagonal terms (blade on itself) dominated the change in stability. Very little mode coupling effect caused by the off-diagonal terms was found.
Source Attribution of Health Benefits from Air Pollution Abatement in Canada and the United States: An Adjoint Sensitivity Analysis
